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Linear complexity profile and correlation measure of interleaved sequences

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Abstract

Let m be a positive integer. We study the linear complexity profile and correlation measure of two interleaved m-ary sequences of length s and t, respectively. In the case that s ≥ 2t or s = t and m is prime we estimate the correlation measure in terms of the correlation measure of the first base sequence and the length of the second base sequence. In this case a relation by Brandstätter and Winterhof immediately implies a lower bound on the linear complexity profile of the interleaved sequence. If m is not a prime, under the same restrictions on s and t, the power correlation measure introduced by Chen and Winterhof takes the role of the correlation measure to obtain lower bounds on the linear complexity profile. Moreover, we show that these restrictions on s and t are necessary, and otherwise the (power) correlation measure can be close to st. However, introducing and estimating the (power) correlation measure with bounded lags we are able to get a lower bound on the linear complexity profile of the interleaved sequence.

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Authors and Affiliations

  1. School of Mathematics & Statistics, Carleton University, Ottawa, K1S 5B6, Canada

    Jing Jane He, Daniel Panario & Qiang Wang

  2. Johann Radon Institute for Computational and Applied Mathematics, Austrian Academy of Sciences, A-4040, Linz, Austria

    Arne Winterhof

Authors
  1. Jing Jane He
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  2. Daniel Panario
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  3. Qiang Wang
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  4. Arne Winterhof
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Corresponding author

Correspondence to Daniel Panario.

Additional information

Daniel Panario and Qiang Wang were partially funded by NSERC of Canada. Arne Winterhof was partially supported by the Austrian Science Fund (FWF): Project F5511-N26, which is a part of the Special Research Program “Quasi-Monte Carlo Methods: Theory and Applications”. Parts of this paper were written during a very pleasant stay of Arne Winterhof to Carleton University. He wishes to thank for hospitality and financial support.

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He, J.J., Panario, D., Wang, Q. et al. Linear complexity profile and correlation measure of interleaved sequences. Cryptogr. Commun. 7, 497–508 (2015). https://doi.org/10.1007/s12095-015-0131-z

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  • DOI: https://doi.org/10.1007/s12095-015-0131-z

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